There is no loss of objectivity, if there is a dispute it can be looked at a ruled on by the refs. So now they are unable to initiate the process, they only get involved in a dispute.

You would think twice about being a player that "think they got fouled on every play" because after being consistently wrong and costing your team a number of points you would be have to be an idiot to continue.

You'd only continue calling them if you were right, in which case they should be being called anyways!

Is there a penalty for being wrong? If there is, that kind of defeats the purpose of being fouled. If not, nothing would deter players from calling fouls. And imagine how choppy the game would be, especially if refs have to sort out every disagreement, not to mention there would be a disagreement on almost every play.

Also imagine how offensive fouls would work, charge is the hardest play to call for a ref, imagine for a player taking a charge. I'm assuming your not including this, but if you are it would be a huge problem. Which actually brings into question which fouls can be called, what about on the floor fouls, when players think it's a shooting foul? Way too many problems.